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Last updated on December 24th, 2024

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Cube Root Of 135

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Foundation
Intermediate
Advance Topics

The cube root of a number is a value that when multiplied by itself three times gives back the original number. We apply the function of cube roots in the fields of engineering, designing, financial mathematics, and many more. Let's learn more about the cube root of 135.

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What Is The Cube Root Of 135?

The cube root can be classified into two categories: perfect cubes and non-perfect cubes. For example, the cube root of 216 is 6 which is a whole number, making it a perfect cube. However, the cube root of 135 is not a whole number. The cube root of 135 is approximately 5.13.

 

The cube root of 135 is represented using the radical sign as ∛135, and can also be written in exponential form as 1351/3. The prime factorization of 135 is 33 × 5. It is also an irrational number where ∛135 cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0. 
 

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Cube Root of 135 by Halley’s Method

Halley’s method is a step-by-step way to find the cube root of a non-perfect cube number. Here, we will find the value of ‘a’ where a3 is the non-perfect cube


∛a≅  x (x3+2a) / (2x3+a) is the formula used in this method. 


As 135 is a non-perfect cube number, it lies between the two perfect cube numbers. Here, ‘a’ lies between 125 (53) and 216 (63)


By applying Halley’s Method, we get.


Step 1: Let the number ‘a’ = 135. Start by taking ‘x’ = 5, as 125 (∛125 = 5) is the nearest perfect cube which is closer to 135


Step 2: Apply the value of ‘a = 135’ and ‘x = 5’ in the formula: 
∛a≅  x (x3+2a) / (2x3+a) 


 Step 3: The formula will be, 
 âˆ›135 ≅  5 (53+2*135) (2*53+135)


Step 4: After simplifying, we get the cube root of 135 as 5.12992784
 

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Important Glossaries for Cube Root Of 135

  • Fraction: It is a way to show a part of something. For example, in the fraction 25 , it means you have 2 out of 5 equal parts. 

 

  • Exponent: It is a smaller number that shows us how many times we multiply the number by itself. For example, in 33, 3 is the exponent, which means we multiply 3 three times.

 

  • Decimal: A number that includes a whole part and a fractional part, which is separated by a dot (.) like 0.5, 3.14, etc., 

 

  • Perfect cube: A number that can be expressed as the product of a whole number multiplied by itself three times, like the cube root of 8 is 2 which is a perfect cube. However, the number cannot be expressed as a whole number when finding its cube root, a non-perfect cube like 135.

 

  • Irrational Number: These are real numbers but cannot be expressed in the form of p/q where both p and q are integers and q ≠ 0.
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